Frequency dependent acoustic, electrical and mechanical feedback identification methods are commonly used in hearing instruments to ensure their stability. Unstable systems due to acoustic feedback tend to significantly contaminate the desired audio input signal with narrow band frequency components, which are often perceived as howl or whistle.
It has been proposed that the stability of a system may be increased by specifically altering its transfer function at critical frequencies [Ammitzboll, 1987]. This can, for example, be achieved with a narrow frequency specific stop-band filter, referred to as a notch-filter [Porayath, 1999]. The disadvantage of this method is that gain has to be sacrificed at and around critical frequencies.
More advanced techniques suggest feedback cancellation by subtracting an estimate of the feedback signal within the hearing instrument. It has been proposed to use a fixed coefficient linear time invariant filter for the feedback path estimate [Dyrlund, 1991]. This method proves to be effective if the feedback path is steady state and, therefore, does not alter over time. However, the feedback path of a hearing aid does vary over time and some kind of tracking ability is often preferred.
Adaptive feedback cancellation has the ability to track feedback path changes over time. It is also based on a linear time invariant filter to estimate the feedback path but its filter weights are updated over time [Engebretson, 1993]. The filter update may be calculated using stochastic gradient algorithms, including some form of the popular Least Mean Square (LMS) or the Normalized LMS (NLMS) algorithms. They both have the property to minimize the error signal in the mean square sense with the NLMS additionally normalizing the filter update with respect to the squared Euclidean norm of some reference signal. A more advanced method combines stochastic gradient algorithms with statistical evaluation of the AFC filter coefficients over time and employs control circuitry in order to ensure the filter coefficients to be updated adequately in noisy situations [Hansen, 1997]. The statistical evaluation is sensible to changes of the phase response and magnitude-frequency response of the feedback path.
Applications like the fitting of a hearing aid require an estimate of the acoustic feedback path of each subject, in particular of the magnitude-frequency response of the acoustic feedback path. In an open-loop configuration, as illustrated in FIG. 1.b), an estimate of the feedback path may be obtained from the frequency response of the adaptive AFC filter (AFC=Adaptive Feedback Cancellation) after convergence of the NLMS algorithm. Background or ambient noise during the measurement influences the convergence behaviour of the NLMS algorithm, contaminates the final state of the AFC filter coefficients and, consequently, yields a distorted estimate of the acoustic feedback path. In order to alleviate this problem, it has been proposed to measure the undesired background noise directly at some defined input using Fourier Transform (FT) based methods. However, these methods require additional algorithms like the Fast Fourier Transform (FFT) and do not reflect the implications on the obtained AFC filter coefficients in a straight forward way.